# Ch 19: Three-Dimensional Geometry: Tutoring Solution

### About This Chapter

## How it works:

- Begin your assignment or other SAT math work.
- Identify the three-dimensional geometry concepts that you're stuck on.
- Find fun videos on the topics you need to understand.
- Press play, watch and learn!
- Complete the quizzes to test your understanding.
- As needed, submit a question to one of our instructors for personalized support.

## Who's it for?

This chapter of our SAT Mathematics Level 2 Tutoring Solution will benefit any student who is trying to learn about three-dimensional geometry to prepare for the subject test. This resource can help students, including those who:

- Struggle with understanding formulas for volume and surface area, coordinates in three dimensions, scale factors of similar figures or any other three-dimensional geometry topic
- Have limited time for studying
- Want a cost effective way to supplement their math learning
- Prefer learning math visually
- Find themselves failing or close to failing their three-dimensional geometry unit
- Cope with ADD or ADHD
- Want to excel on the SAT Mathematics Level 2 subject test
- Don't have access to their math teacher outside of class

## Why it works:

**Engaging Tutors**: We make learning about three-dimensional geometry simple and fun.**Cost Efficient**: For less than 20% of the cost of a private tutor, you'll have unlimited access 24/7.**Consistent High Quality**: Unlike a live math tutor, these video lessons are thoroughly reviewed.**Convenient**: Imagine a tutor as portable as your laptop, tablet or smartphone. Learn about three-dimensional geometry on the go!**Learn at Your Pace**: You can pause and re-watch lessons as often as you'd like, until you master the material.

## Learning Objectives

- Study the process for solving visualizing geometry problems.
- Learn to calculate volumes of basic shapes.
- Find out about the volume of prisms and pyramids.
- Determine the volume of cylinders, cones and spheres.
- Learn to find surface area and apply scale factors to perimeter, area and volume of similar figures.

### 1. How to Solve Visualizing Geometry Problems

A picture is worth a thousand words, but sometimes drawing that picture can be like doing origami with your eyes closed. Practice translating complex problems into simple, meaningful images in this lesson.

### 2. How to Calculate the Volumes of Basic Shapes

Squares pegs = square holes. Triangular pegs = triangular holes. But where does a sphere go? In this lesson, review volumes of common shapes while contrasting a sphere and a cylinder - after all, they both go into the circular hole... right?

### 3. Volume of Prisms and Pyramids

In this lesson, we'll learn about prisms and pyramids. We'll look at the different types of prisms and pyramids, as well as practice calculating volume for each shape.

### 4. Volume of Cylinders, Cones, and Spheres

In this lesson, we'll learn about the volume formulas for cylinders, cones and spheres. We'll also practice using the formula in a variety of real-world examples where knowing how to calculate volume is helpful.

### 5. What is Surface Area? - Definition & Formulas

In this lesson, you use general and specific formulas to learn how to find the surface area of three-dimensional shapes, such as cubes, prisms, spheres, cones and cylinders.

### 6. How to Plot Points in Three Dimensions

In this lesson, we'll look at what a three-dimensional coordinate system looks like. After that, we'll learn how to plot points in three dimensions and look at a couple of examples of the process.

### 7. Applying Scale Factors to Perimeter, Area, and Volume of Similar Figures

How do shapes change sizes yet retain their proportions and similarities to other shapes? In this lesson, we'll look at what a scale factor is and how to apply it. We'll consider scale factors with regards to three different aspects of similar shapes: perimeter, area and volume.

### 8. Surface Area of a Hexagonal Prism

In this lesson, we will develop the equation for the surface area of a hexagonal prism and show how this relates to wax production in beehives. Using the equation, we will calculate the total surface area of a typical beehive cell.

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### Other Chapters

Other chapters within the SAT Subject Test Mathematics Level 2: Tutoring Solution course

- SAT Math Level 2 Structure & Strategy: Tutoring Solution
- Basic Math Review: Tutoring Solution
- Square Roots: Tutoring Solution
- Basic Algebraic Expressions in Math: Tutoring Solution
- Exponents in Math: Tutoring Solution
- Vectors: Tutoring Solution
- Linear Equations & Inequalities in Algebra: Tutoring Solution
- Absolute Value Equations & Inequalities: Tutoring Solution
- Polynomials in Algebra: Tutoring Solution
- Functions in Math: Tutoring Solution
- Rational Expressions in Algebra: Tutoring Solution
- Matrices: Tutoring Solution
- Sequences and Series in Math: Tutoring Solution
- Exponentials and Logarithms in Math: Tutoring Solution
- Complex Numbers in Math: Tutoring Solution
- Coordinate Geometry Basics: Tutoring Solution
- Graphing Linear Equations & Inequalities: Tutoring Solution
- Advanced Coordinate Geometry: Tutoring Solution
- Overview of Trigonometry: Tutoring Solution
- Probability, Combinations & Permutations: Tutoring Solution
- Working with Data & Statistics: Tutoring Solution
- Logic: Tutoring Solution
- Limits in Math: Tutoring Solution